An important thing to note: The Avenger's armor rating drops to 50% when in combat (on Steam version, this applies also when freezed or stunned), allowing them to take some physical damage during fights.

One thing to note is that Reg'son, Lynn, and Renegades are completely immune to the Avengers' curse explosions, being that they are all Twilight Elves.

Strategy

The blasting curse can sometimes prove to be an unexpected (and welcome) help against swarms of Gloomies: if a Gloomy is cursed, then the entire swarm is doomed, as the curse's damage is high enough to kill them even on Veteran difficulty.

Place your soldiers backwards, behind lines of towers to quickly clear out the cursed enemies before they reach melee combat. Wild Magus is highly effective, thanks to her ability to silence the Twilight Avenger, magical damage output and instant kill spell that further damage the surrounding twilight elves.

Forest Keepers can support your soldiers and hold their own against explosions with Circle of Life, while also damage the Twilight Avenger with the True Damage of Ancient Oak Spears and slow down the living bombs with Eerie Gardener. Put them near your units to fully utilize their potentials.

Wild Magus has extremely fast fire rate, and the tower itself can actually kill Twilight Avengers in a good time. Boulder is really helpful, especially, Weirdwood.